Assessment of empirical formulae for determining the hydraulic conductivity of glass beads

Empirical formulae are often used in practice to quickly and cheaply determine the hydraulic conductivity of soil. Numerous relations based on dimensional analysis and experimental measurements have been published for the determination of hydraulic conductivity since the end of 19th century. In this paper, 20 available empirical formulae are listed, converted and re-arranged into SI units. Experimental research was carried out concerning hydraulic conductivity for three glass bead size (diameters 0.2 mm, 0.5 mm and 1.0 mm) and variable porosity. The series of experiments consisted of 177 separate tests conducted in order to obtain relevant statistical sets. The validity of various published porosity functions and empirical formulae was verified with the use of the experimental data obtained from the glass beads. The best fit was provided by the porosity function n3/(1-n)2. In the case of the estimation of the hydraulic conductivity of uniform glass beads, the best fit was exhibited by formulae published by Terzaghi, Kozeny, Carman, Zunker and Chapuis et al.

Functionally Heterogeneous Porous Scaffold Design for Tissue Engineering

Most of the current tissue scaffolds are mainly designed with homogeneous porosity which does not represent the spatial heterogeneity found in actual tissues. Therefore engineering a realistic tissue scaffolds with properly graded properties to facilitate the mimicry of the complex elegance of native tissues are critical for the successful tissue regeneration. In this work, novel bio-mimetic heterogeneous porous scaffolds have been modeled. First, the geometry of the scaffold is extracted along with its internal regional heterogeneity. Then the model has been discretized with planner slices suitable for layer based fabrication. An optimum filament deposition angle has been determined for each slice based on the contour geometry and the internal heterogeneity. The internal region has been discritized considering the homogeneity factor along the deposition direction. Finally, an area weight based approach has been used to generate the spatial porosity function that determines the filament deposition location for desired bio-mimetic porosity. The proposed methodology has been implemented and illustrative examples are provided. The effective porosity has been compared between the proposed design and the conventional homogeneous scaffolds. The result shows a significant error reduction towards achieving the bio-mimetic porosity in the scaffold design and provides better control over the desired porosity level. Moreover, sample designed structures have also been fabricated with a NC motion controlled micro-nozzle biomaterial deposition system.